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Free Surface Elevation of Solitary Waves Formula

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Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions. Check FAQs

η = H w \cdot (\frac{u}{\sqrt{[g] \cdot d c} \cdot (\frac{H w}{d c})})

η - Free Surface Elevation?H_w - Height of the Wave?u - Particle Velocity?d_c - Water Depth for Cnoidal Wave?[g] - Gravitational acceleration on Earth?

Free Surface Elevation of Solitary Waves Example

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Here is how the Free Surface Elevation of Solitary Waves equation looks like with Values.

Here is how the Free Surface Elevation of Solitary Waves equation looks like with Units.

Here is how the Free Surface Elevation of Solitary Waves equation looks like.

25.5464 = 14 \cdot (\frac{20}{\sqrt{9.8066 \cdot 16} \cdot (\frac{14}{16})})

25.5464m = 14m \cdot (\frac{20m/s}{\sqrt{9.8066m/s² \cdot 16m} \cdot (\frac{14m}{16m})})

25.5464 = 14 \cdot (\frac{20}{\sqrt{9.8066 \cdot 16} \cdot (\frac{14}{16})})

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Free Surface Elevation of Solitary Waves Solution

Follow our step by step solution on how to calculate Free Surface Elevation of Solitary Waves?

FIRST Step Consider the formula

η = H w \cdot (\frac{u}{\sqrt{[g] \cdot d c} \cdot (\frac{H w}{d c})})

Next Step Substitute values of Variables

∴

η = 14m \cdot (\frac{20m/s}{\sqrt{[g] \cdot 16m} \cdot (\frac{14m}{16m})})

Next Step Substitute values of Constants

∴

η = 14m \cdot (\frac{20m/s}{\sqrt{9.8066m/s² \cdot 16m} \cdot (\frac{14m}{16m})})

Next Step Prepare to Evaluate

∴

η = 14 \cdot (\frac{20}{\sqrt{9.8066 \cdot 16} \cdot (\frac{14}{16})})

Next Step Evaluate

∴

η = 25.5463965424847m

LAST Step Rounding Answer

∴

η = 25.5464m

Free Surface Elevation of Solitary Waves Formula Elements

Variables

Constants

Functions

Free Surface Elevation

Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions.

Symbol: η

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Free Surface Elevation

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

Particle Velocity

Particle Velocity refers to the velocity at which water particles move as a result of the passage of waves or currents.

Symbol: u

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Particle Velocity

Water Depth for Cnoidal Wave

Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

Symbol: d_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth for Cnoidal Wave

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Cnoidal Wave Theory category

Go Distance from Bottom to Wave Trough

y t = d c \cdot ((\frac{y c}{d c}) - (\frac{H w}{d c}))

Go Distance from Bottom to Crest

y c = d c \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}))

Go Trough to Crest Wave Height

H w = d c \cdot ((\frac{y c}{d c}) - (\frac{y t}{d c}))

Go Complete Elliptic Integral of Second Kind

E k = - ((((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1) \cdot \frac{3 \cdot λ^{2}}{(16 \cdot {d c}^{2}) \cdot K k}) - K k)

How to Evaluate Free Surface Elevation of Solitary Waves?

Free Surface Elevation of Solitary Waves evaluator uses Free Surface Elevation = Height of the Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of the Wave/Water Depth for Cnoidal Wave))) to evaluate the Free Surface Elevation, The Free Surface Elevation of Solitary Waves formula is defined as the surface elevation of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. Free Surface Elevation is denoted by η symbol.

How to evaluate Free Surface Elevation of Solitary Waves using this online evaluator? To use this online evaluator for Free Surface Elevation of Solitary Waves, enter Height of the Wave (H_w), Particle Velocity (u) & Water Depth for Cnoidal Wave (d_c) and hit the calculate button.

FAQs on Free Surface Elevation of Solitary Waves

What is the formula to find Free Surface Elevation of Solitary Waves?

The formula of Free Surface Elevation of Solitary Waves is expressed as Free Surface Elevation = Height of the Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of the Wave/Water Depth for Cnoidal Wave))). Here is an example- 25.5464 = 14*(20/(sqrt([g]*16)*(14/16))).

How to calculate Free Surface Elevation of Solitary Waves?

With Height of the Wave (H_w), Particle Velocity (u) & Water Depth for Cnoidal Wave (d_c) we can find Free Surface Elevation of Solitary Waves using the formula - Free Surface Elevation = Height of the Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of the Wave/Water Depth for Cnoidal Wave))). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Free Surface Elevation of Solitary Waves be negative?

Yes, the Free Surface Elevation of Solitary Waves, measured in Length can be negative.

Which unit is used to measure Free Surface Elevation of Solitary Waves?

Free Surface Elevation of Solitary Waves is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Free Surface Elevation of Solitary Waves can be measured.

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Free Surface Elevation of Solitary Waves Formula

Free Surface Elevation of Solitary Waves Example

Free Surface Elevation of Solitary Waves Solution

Free Surface Elevation of Solitary Waves Formula Elements

Other formulas in Cnoidal Wave Theory category

How to Evaluate Free Surface Elevation of Solitary Waves?

FAQs on Free Surface Elevation of Solitary Waves

Variable Name